//g++ abgabe6.cpp -std=c++14 -o abgabe6
// ./abgabe6
// Pauline Maas, Ariane Ufer

#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <math.h>
#include <complex>
#include <vector>
using namespace std;
#ifndef M_PI
#define M_PI           3.14159265358979323846
#endif
typedef struct {
    long n;
    double b, a, beta, alpha;
    double tmin, tmax,h,tl,signalLenght;
    int m;
    int sign;
} fft_param;


//Pseudo-Zufallszahlen-Generator
//Part of a C-program for MT19937, with initialization improved 2002/1/26.
//Coded by Takuji Nishimura and Makoto Matsumoto.

/* Period parameters */  
#define N 624
#define M 397
#define MATRIX_A 0x9908b0dfUL   /* constant vector a */
#define UPPER_MASK 0x80000000UL /* most significant w-r bits */
#define LOWER_MASK 0x7fffffffUL /* least significant r bits */

static unsigned long mt[N]; /* the array for the state vector  */
static int mti=N+1; /* mti==N+1 means mt[N] is not initialized */

/* initializes mt[N] with a seed */
void init_genrand(unsigned long s)
{
    mt[0]= s & 0xffffffffUL;
    for (mti=1; mti<N; mti++) {
        mt[mti] = 
	    (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti); 
        /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
        /* In the previous versions, MSBs of the seed affect   */
        /* only MSBs of the array mt[].                        */
        /* 2002/01/09 modified by Makoto Matsumoto             */
        mt[mti] &= 0xffffffffUL;
        /* for >32 bit machines */
    }
}

/* initialize by an array with array-length */
/* init_key is the array for initializing keys */
/* key_length is its length */
/* slight change for C++, 2004/2/26 */
void init_by_array(unsigned long init_key[], int key_length)
{
    int i, j, k;
    init_genrand(19650218UL);
    i=1; j=0;
    k = (N>key_length ? N : key_length);
    for (; k; k--) {
        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525UL))
          + init_key[j] + j; /* non linear */
        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
        i++; j++;
        if (i>=N) { mt[0] = mt[N-1]; i=1; }
        if (j>=key_length) j=0;
    }
    for (k=N-1; k; k--) {
        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL))
          - i; /* non linear */
        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
        i++;
        if (i>=N) { mt[0] = mt[N-1]; i=1; }
    }

    mt[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */ 
}

/* generates a random number on [0,0xffffffff]-interval */
unsigned long genrand_int32(void)
{
    unsigned long y;
    static unsigned long mag01[2]={0x0UL, MATRIX_A};
    /* mag01[x] = x * MATRIX_A  for x=0,1 */

    if (mti >= N) { /* generate N words at one time */
        int kk;

        if (mti == N+1)   /* if init_genrand() has not been called, */
            init_genrand(5489UL); /* a default initial seed is used */

        for (kk=0;kk<N-M;kk++) {
            y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
            mt[kk] = mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1UL];
        }
        for (;kk<N-1;kk++) {
            y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
            mt[kk] = mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1UL];
        }
        y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
        mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];

        mti = 0;
    }
  
    y = mt[mti++];

    /* Tempering */
    y ^= (y >> 11);
    y ^= (y << 7) & 0x9d2c5680UL;
    y ^= (y << 15) & 0xefc60000UL;
    y ^= (y >> 18);

    return y;
}

/* generates a random number on [0,1) with 53-bit resolution*/
double genrand_res53(void) 
{ 
    unsigned long a=genrand_int32()>>5, b=genrand_int32()>>6; 
    return(a*67108864.0+b)*(1.0/9007199254740992.0); 
} 
// End of C-program for MT19937




complex<double> expo(fft_param *fp,int k) {
    int sign = fp->sign;
    int n=fp->n;
    return exp(sign*2.0 * M_PI * 1i* ((double)(k/n)));
    
}

vector<complex<double>> fourierTrafo(fft_param *fp, vector<complex<double>> x) {
    long n = x.size(); //Länge des x vektors 
    int sign=fp->sign;
    vector<complex<double>> gerPkt(n / 2); //Vektoren um x in gerade und ungerade Teile aufzuteilen
    vector<complex<double>> ungerPkt(n / 2); //Haben dann Länge n/2
    
    if (n == 1) {
        
        return x;
    } else {
        //Aufteilen
        for (int k = 0; k < n / 2; k++) {
            gerPkt[k] = x[2 * k];
            ungerPkt[k] = x[2 * k + 1];
        }
        
        vector<complex<double>> ftger = fourierTrafo(fp, gerPkt);  //rekursives Aufrufen der Funktion um weiter zu Teilen
        vector<complex<double>> ftunger = fourierTrafo(fp, ungerPkt); 
        vector<complex<double>> out(n);
        
        for (int k = 0; k < n / 2; k++) {
            //In out ergebnis nach FFT routine Speichern
            if(sign==-1){
                out[k] = (ftger[k] + ftunger[k] * expo(fp,k));
                out[k + n / 2] = (ftger[k] - ftunger[k] *expo(fp,k));
            }
            else{
                out[k] = (ftger[k] + ftunger[k] * expo(fp,k));
                out[k + n / 2] = (ftger[k] - ftunger[k] *expo(fp,k));
            }
        }
        
        return out;
    }
}
 
vector<complex<double>> makeS(fft_param *fp){
    double h=fp->h; //Variabeln aus struct holen
    double tmax=fp->tmax;
    double tmin=fp->tmin;;
    double t;
    double tl=fp->tl;
    double alpha=fp->alpha;
    int n=fp->n;
    vector<complex<double>> s(n); //Vektor zum speichern von s
    for(int k=0;k<n;k++){
        t=tmin+k*h;
        //TODO s ist nicht geschiftet
        if (t >= 0 && t <= fp->signalLenght){
            s[k]=sin(2*M_PI*alpha*(t-tl)); //s berechnen 
            
        }
        else{
            s[k]=0;
        }
        
    }
    return s;
}
vector<complex<double>> makeE(fft_param *fp){
    double h=fp->h; //Variabeln aus struct holen
    double tmax=fp->tmax;
    double tmin=fp->tmin;
    double t;
    double beta=fp->beta;
    double alpha=fp->alpha;
    double tl=fp->tl;
    double a=fp->a;
    double b=fp->b;
    int n=fp->n;
    vector<complex<double>> e(n); //Vektor zum speichern von e
    //vector<complex<double>> s=makeS(fp); //Vektor s wird benötigt
    //FILE *fp3 = fopen("H10_2_30.txt" ,"w");
    for(int k=0;k<n;k++){
        t=tmin+k*h;
        e[k]=b*sin(2*M_PI*beta*t)+ 2*a*(genrand_res53()-0.5); //e berechnen
        
        if (t-tl >= 0 && t-tl <= fp->signalLenght){
            e[k]+=sin(2*M_PI*alpha*(t-tl)); //s berechnen 
            
        }
        //fprintf(fp3,"%f\t%f\n",t,pow(e[k].real(),2));
        //printf("%f\t%f\n",t,pow(e[k].real(),2));
        //printf("%f\t%f\t%f\n",t,e[k].real(),e[k].imag());
    }
    //fclose(fp3);
    return e;
}
vector<complex<double>> aufgabe3 (fft_param *fp){
    double h=fp->h; //Varabeln aus Struct holen
    double tmin=fp->tmin;
    double tmax=fp->tmax;
    double t=tmin;
    int n=fp->n;
    vector<complex<double>> e=makeE(fp); //e und s berechnen
    vector<complex<double>> s=makeS(fp);
    vector<complex<double>> Fe=fourierTrafo(fp,e); //e Fouriertransformieren
    
    vector<complex<double>> Fs=fourierTrafo(fp,s); //s Fouriertransformieren
    vector<complex<double>> FFes(n); //Vektor machen zum speichern
    
    for(int k=0;k<n;k++){
        //Hier Fouriertransformation von e mal Fouriertransformation von s komplex konjugiert berechnen
        FFes[k]=Fe[k]*conj(Fs[k]);
        
    }
    fft_param fps=*fp; //Sign im struct ändern
    fps.sign=-1;
    vector<complex<double>> FFFes=fourierTrafo(&fps, FFes); //Rücktransformation des Produkts

    FILE *fpPlot =fopen("esPlot.csv","w");
    for(int k = 0; k<n; k++){
    	fprintf(fpPlot, "%f\t%f\t%f\n", tmin+k*h, s[k].real(), e[k].real());
    }

    return FFFes;
    //init_genrand((long)seed);
}
void plotAufgabe3(fft_param *fp){
    int n = fp->n;
    double tmin=fp->tmin;
    double h=fp->h;
    vector<complex<double>> es = aufgabe3(fp);
    FILE *fp4 =fopen("es4.csv","w");
    for (int k=0;k<n;k++){
        //printf("%f\n", norm(es[k]));
        
        fprintf(fp4,"%f\t%f\n", tmin+k*h, norm(es[k]/(double)N));
        
    }
    
}
int main(){
    long seed = 57291; // beliebigen Wert gewählt
    init_genrand(seed); //rufe am Anfang mit einem festen Wert auf für reproduzierbare Ergebnise
    
    
    fft_param fp;
    fp.n= pow(2,13);
    fp.tmin=0;
    fp.tmax = 100;
    fp.h=(fp.tmax-fp.tmin)/fp.n;
    fp.sign=1;
    fp.alpha=10;
    fp.beta=1;
    fp.a=0.5;
    fp.b=0.50;
    fp.tl=50;
    fp.signalLenght = 5;
    //test(&fp);
    plotAufgabe3(&fp);
    //printf("%f\n",genrand_res53());
    
    //H10.2
    fp.h=0.001; //Schrittweite der Zeit für Plot
    fp.n=100/0.001; // plotte e(t) bis für die Zeit tmin bis tmin + 100
    //makeE(&fp);
    
    
}